A particle moves along a straight line such t | vedclass

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Question

(A) The displacement is given by $s = t^3 - 3t^2 + 2$.The velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{ds}{dt

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(A) The displacement is given by $s = t^3 - 3t^2 + 2$.The velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{ds}{dt} = 3t^2 - 6t$.The acceleration $a$ is the derivative of velocity with respect to time: $a = \frac{dv}{dt} = \frac{d^2s}{dt^2} = 6t - 6$.Set the acceleration to zero to find the time $t$:$6t - 6 = 0 \implies t = 1 \, s$.Now,substitute $t = 1 \, s$ into the displacement equation to find the displacement at that instant:$s = (1)^3 - 3(1)^2 + 2 = 1 - 3 + 2 = 0 \, m$.

Column-$I$	Column-$II$
$(1)$ Acceleration is positive	$(a)$ Speed of the particle decreases
$(2)$ Acceleration is negative	$(b)$ Speed of the particle increases
	$(c)$ Speed of the particle keeps changing

$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = (t^3 - 3t^2 + 2) \, m$. The displacement when the acceleration becomes zero is ........ $m$.

Similar Questions

If velocity and acceleration are in opposite directions in one-dimensional motion,what happens to the magnitude of velocity?

The acceleration of a train between two stations is shown in the figure. The maximum speed of the train is $............\,m/s$.

Match the items in Column-$I$ with the items in Column-$II$ correctly.

Column-$I$ Column-$II$

$(1)$ Acceleration is positive $(a)$ Speed of the particle decreases

$(2)$ Acceleration is negative $(b)$ Speed of the particle increases

$(c)$ Speed of the particle keeps changing

The velocity $(v)-$ time $(t)$ plot of the motion of a body is shown below:
The acceleration $(a)-$ time $(t)$ graph that best suits this motion is:

Each of the three graphs represents acceleration versus time for an object that already has a positive velocity at time $t_1$. Which graphs show an object whose speed is increasing for the entire time interval between $t_1$ and $t_2$?

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